Abstract
Surveys were used to examine mathematics teachers (15) on their ability to solve similarity problems and on their likely implementation of lesson objectives for teaching similarity. All correctly solved a similarity problem requiring a traditional static perspective, but 7 out of 15 failed to correctly solve a problem that required a more transformational perspective. A set of 10 lesson objectives on similarity were composed using Geometry textbooks, using the Common Core State Standards (CCSS), (NGA Center and CCSSO 2011), and using some generated by the authors. When asked to select from the list of objectives the ones they would most likely implement, teachers favored traditional textbook objectives that might be presented using a static perspective, rather than similarity transformations, manipulatives, or technology that might support a more transformational perspective. In fact, these were among the objectives most likely not included in their lesson plans.
Highlights
Euclidean geometry normally places congruence before similarity so there may be a tendency to think of similarity as a less important extension of congruence (Usiskin, Peressini, Marchisotto, & Stanley, 2003), but being able to apply concepts of similarity is a critical aspect of middle and high school mathematics.There have been suggestions that similarity needs to be presented even earlier in the curriculum
Implementation of a transformational approach to teaching congruence and similarity is recommended by both the Principles and Standards for School Mathematics (NCTM, 2000) and the Common Core State Standards (CCSS),(NGA Center and CCSSO 2011).Seago, et al (2013) argue that engaging teachers in a transformational approach to similarity is an urgent but largely
Over time support for a transformational approach grew with the publication by the National Council of Teachers of Mathematics (NCTM) of the Curriculum and Evaluation Standards (NCTM, 1989) and the Principles and Standards for School Mathematics (NCTM, 2000)which states that instructional programs prekindergarten through 12th grade should enable all students to apply transformations to analyze mathematical situations
Summary
Euclidean geometry normally places congruence before similarity so there may be a tendency to think of similarity as a less important extension of congruence (Usiskin, Peressini, Marchisotto, & Stanley, 2003), but being able to apply concepts of similarity is a critical aspect of middle and high school mathematics.There have been suggestions that similarity needs to be presented even earlier in the curriculum. Implementation of a transformational approach to teaching congruence and similarity is recommended by both the Principles and Standards for School Mathematics (NCTM, 2000) and the Common Core State Standards (CCSS),(NGA Center and CCSSO 2011).Seago, et al (2013) argue that engaging teachers in a transformational approach to similarity is an urgent but largely. More recently the Common Core State Standards (NGA Center and CCSSO 2011) defined what students should understand and be able to do in their study of mathematics. This set of standards advocates strongly for a transformational approach to the study of congruence, similarity, and symmetry. Is one of the standards that endorses a transformational perspective
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